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You have learnt that a travelling wave in one dimension is represented by a function y = f (x, t) where x and t must appear in the combination x – v t or x + v t, i.e. y = f (x ± v t). Is the converse true? Examine if the following functions for y can possibly represent a travelling wave : (a) `(x – vt )^2` (b) `log [(x + vt)/x_0]` (c) 1/(x +

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A bat emits ultrasonic sound of frequency 1000 kHz in air. If the sound meets a water surface, what is the wavelength of (a) the reflected sound, (b) the transmitted sound? Speed of sound in air is 340 m `s^(–1)` and in water 1486 m

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A hospital uses an ultrasonic scanner to locate tumours in a tissue. What is the wavelength of sound in the tissue in which the speed of sound is 1.7 km `s^(–1)` ? The operating frequency of the scanner is 4.2

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A transverse harmonic wave on a string is described by. y(x, t) = 3.0 sin (36 t + 0.018 x + π/4) where x and y are in cm and t in s. The positive direction of x is from left to right. (a) Is this a travelling wave or a stationary wave ? If it is travelling, what are the speed and direction of its propagation ? (b) What are its amplitude and frequency ? (c) What is the initial phase at the origin ? (d) What is the least distance between two successive crests in the wave

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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For the wave described in Exercise 15.8, plot the displacement (y) versus (t) graphs for x = 0, 2 and 4 cm. What are the shapes of these graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another: amplitude, frequency or phase

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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For the travelling harmonic wave y(x, t) = 2.0 cos 2π (10t – 0.0080 x + 0.35) where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of (a) 4 m, (b) 0.5 m, (c) λ/2, (d)

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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The transverse displacement of a string (clamped at its both ends) is given by `y(x, t) = 0.06 sin((2π)/3x) cos (120 πt)` where x and y are in m and t in s.The length of the string is 1.5 m and its mass is `3.0 ×10^(–2)` kg. Answer the following : (a) Does the function represent a travelling wave or a stationary wave? (b) Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave ? (c) Determine the tension in the

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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(i) For the wave on a string described in Exercise 15.11, do all the points on the string oscillate with the same (a) frequency, (b) phase, (c) amplitude? Explain your answers. (ii) What is the amplitude of a point 0.375 m away from one

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a travelling wave, (ii) a stationary wave or (iii) none at all: (a) y = 2 cos (3x) sin (10t) (b) `y = 2sqrt(x-vt)` (c) y = 3 sin (5x – 0.5t) + 4 cos (5x – 0.5t) (d) y = cos x sin t + cos 2x sin

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is `3.5 × 10^(–2)` kg and its linear mass density is `4.0 × 10^(–2)` kg `m^(–1)`. What is (a) the speed of a transverse wave on the string, and (b) the tension in the

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A metre-long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the tube length is 25.5 cm or 79.3 cm. Estimate the speed of sound in air at the temperature of the experiment. The edge effects may be

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be 2.53 kHz. What is the speed of sound in

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 430 Hz source ? Will the same source be in resonance with the pipe if both ends are open? (speed of sound in air is 340 m

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Two sitar strings A and B playing the note ‘Ga’ are slightly out of tune and produce beats of frequency 6 Hz. The tension in the string A is slightly reduced and the beat frequency is found to reduce to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Explain why (or how): (a) in a sound wave, a displacement node is a pressure antinode and vice versa, (b) bats can ascertain distances, directions, nature, and sizes of the obstacles without any “eyes”, (c) a violin note and sitar note may have the same frequency, yet we can distinguish between the two notes, (d) solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases, and (e) the shape of a pulse gets distorted during propagation in a dispersive

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A train, standing at the outer signal of a railway station blows a whistle of frequency 400 Hz in still air. (i) What is the frequency of the whistle for a platform observer when the train (a) approaches the platform with a speed of 10 m `s^(–1)`, (b) recedes from the platform with a speed of 10 m `s^(–1)`? (ii) What is the speed of sound in each case ? The speed of sound in still air can be taken as 340 m

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A train, standing in a station-yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10 m `s^(–1)`. What are the frequency, wavelength, and speed of sound for an observer standing on the station’s platform? Is the situation exactly identical to the case when the air is still and the observer runs towards the yard at a speed of 10 m `s^(–1)`? The speed of sound in still air can be taken as 340 m

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A travelling harmonic wave on a string is described by y(x, t) = 7.5 sin (0.0050x +12t + π/4) (a)what are the displacement and velocity of oscillation of a point at x = 1 cm, and t = 1 s? Is this velocity equal to the velocity of wave propagation? (b)Locate the points of the string which have the same transverse displacements and velocity as the x = 1 cm point at t = 2 s, 5 s and 11

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A narrow sound pulse (for example, a short pip by a whistle) is sent across a medium. (a) Does the pulse have a definite (i) frequency, (ii) wavelength, (iii) speed of propagation? (b) If the pulse rate is 1 after every 20 s, (that is the whistle is blown for a split of second after every 20 s), is the frequency of the note produced by the whistle equal to 1/20 or 0.05 Hz

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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One end of a long string of linear mass density 8.0 × 10–3 kg m–1 is connected to an electrically driven tuning fork of frequency 256 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90 kg. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At t = 0, the left end (fork end) of the string x = 0 has zero transverse displacement (y = 0) and is moving along positive y-direction. The amplitude of the wave is 5.0cm. Write

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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