What is the nature of water waves produced by a motorboat sailing in water ?

Show that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3loops and 4loops, the frequencies are in the ratio 1:2:3:4.

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 os 1.7 kms^-1? The operating frequency of the scanner is 4.2 MHz.

A sonometer wire is vibrating in resonance with a tuning fork. Keeping the tension applied same, the length of the wire is doubled. Under what conditions would the tuning fork still be in resonance with the wire?

What frequency of the sound you hear coming directly from the siren?

Equation of a plane progressive wave is given by y = 0.6 sin\(2\pi \left( t-\frac { x }{ 2 } \right) \) On reflection from a denser medium, its amplitude becomes 2/3 of the amplitude of  incident wave. What will be equation of reflected wave?

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 .

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 + vt i.e., y = f (x ± vt). Is the converse true? That is, does every function of (x - vt) or (x + vt) represent a travelling wave? Examine, if the following functions for y can possibly represent a travelling wave?
(a) (x-vt)² (b) \(log[\frac{(x+vt)}{x_{0}}]\) (c) \(\frac{1}{x+vt}\)

A light wave is reflected from the mirror. The incident and the reflected waves superimpose to form
stationary wave, but the nodes and anti-nodes are not seen. Why?

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)

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).

(a) If the successive overtones of vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamental note?
(b) If the amplitude of a sound wave is tripled, by how many dB will the intensity level increases?

Ritesh is a very good flute player but he did not know how he gets the different tanned sound by closing and opening the flute holes. He went to his music teacher in the school and asked him to explain the reason of getting the different tanned sound from the flute player. His music teacher explained that when the air is pushed into the flute player pipe, nodes and antinodes are formed and by closing and opening the holes at different heights, we hear the different tanned sound. Ritesh was happy to hear it.
(i) What values were shown by Ritesh?
(ii) On a certain day, speed of sound in air is 350 m/s. What is the frequency of fundamental note in a closed pipe of length 0.5 m? Also find the frequency of second overtone.

Given below are some examples of wave motion. State in each case if the wave motion is transverse, longitudinal or a combination of both:
(a) Motion of a kink in a longitudinal spring produced by displacing one end of the spring sideways.
(b) Waves produced in a cylinder containing a liquid by moving its piston back and forth.
(c) Waves produced by a motorboat sailing in water.
(d) Ultrasonic waves in air produced by a vibrating quartz crystal.

A wave travelling along a string is described by, y(x, t) = 0.005 sin (80.0 x - 3.0 t), in which the numerical constants are in SI units (0.005 m, 80.0 rad m^–1, and 3.0 rad s^–1). Calculate
(i) wavelength

 A train, standing in 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 \(10{ ms }^{ -1 }\). 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 \(10{ ms }^{ -1 }\)? The speed of sound in still air can be taken as 340\({ ms }^{ -1 }\)

The amplitude of a wave disturbed propagating in the positive x direction is given by \(y=\frac{1}{1+x^{2}}\) at t = 0 and \(y=\frac{1}{[1+(x-1)^{2}]}\) at t=2s where x and y in metre. The shape of disturbance does not change during the propagation. What is the velocity of the wave?