A stone dropped from the top of a tower of height 300 m splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is 340 m $s^{-1}$ ? ($g$ = 9.8 m $s^{-2}$)

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) $y = 2 \cos(3x) \sin(10t)$

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 $s^{-1}$.

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 MHz.

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 $s^{-1}$

The transverse displacement of a string (clamped at its both ends) is given by $y(x, t) = 0.06 \sin(\frac{2\pi x}{3}) \cos(120 \pi t)$ where $x$ and $y$ are in m and $t$ in s. The length of the string is 1.5 m and its mass is $3.0 \times 10^{-2}$ kg. Answer the following : (a) Does the function represent a travelling wave or a stationary wave?

Use the formula $v = \sqrt{\frac{\gamma P}{\rho}}$ to explain why the speed of sound in air (a) is independent of pressure,

A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at 20 °C = 343 m $s^{-1}$.

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

The transverse displacement of a string (clamped at its both ends) is given by $y(x, t) = 0.06 \sin(\frac{2\pi x}{3}) \cos(120 \pi t)$ where $x$ and $y$ are in m and $t$ in s. The length of the string is 1.5 m and its mass is $3.0 \times 10^{-2}$ kg. Answer the following : (b) Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave ?

A train, standing at the outer signal of a railway station blows a whistle of frequency 400 Hz in still air. (ii) What is the speed of sound in each case ? The speed of sound in still air can be taken as 340 m $s^{-1}$.

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. $y = f (x \pm v t)$. Is the converse true? Examine if the following functions for $y$ can possibly represent a travelling wave : (a) $(x - vt)^2$

The transverse displacement of a string (clamped at its both ends) is given by $y(x, t) = 0.06 \sin(\frac{2\pi x}{3}) \cos(120 \pi t)$ where $x$ and $y$ are in m and $t$ in s. The length of the string is 1.5 m and its mass is $3.0 \times 10^{-2}$ kg. Answer the following : (c) Determine the tension in the string.

Use the formula $v = \sqrt{\frac{\gamma P}{\rho}}$ to explain why the speed of sound in air (c) increases with humidity.

A transverse harmonic wave on a string is described by $y(x, t) = 3.0 \sin (36 t + 0.018 x + \pi/4)$ 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 ?

For the wave on a string described in Exercise 15.11, do all the points on the string oscillate with the same (a) frequency? Explain your answers.

For the travelling harmonic wave $y(x, t) = 2.0 \cos 2\pi (10t – 0.0080 x + 0.35)$ 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,

Explain why (or how): (e) the shape of a pulse gets distorted during propagation in a dispersive medium.

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 $s^{-1}$).

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. $y = f (x \pm v t)$. Is the converse true? Examine if the following functions for $y$ can possibly represent a travelling wave : (c) $\frac{1}{(x + vt)}$