Find the change in the volume of 1.0 liter kerosene when it is subjected to an extra pressure of 2.0 × 10⁵ N m^-2 from the following data. Density of kerosene = 800 kg m^-3 and speed of sound in kerosene 1330 m s^-1.

For the harmonic travelling wave y = 2 cos 2π (10t–0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of,

(a) 4 m

(b) 0.5 m

(c)

(d) (at a given instant of time)

(e) What is the phase difference between the oscillation of a particle located at x = 100cm, at t = T s and t = 5 s?

In the given progressive wave y = 5 sin (100πt – 0.4πx) where y and x are in m, t is in s. What is the

(a) amplitude

(b) wave length

(c) frequency

(d) wave velocity

(e) particle velocity amplitude.

Given below are some functions of x and t to represent the displacement of an elastic wave.

(a) y = 5 cos (4x) sin (20t)

(b) y = 4 sin (5x – t/2) + 3 cos (5x – t/2)

(c) y = 10 cos [(252 – 250) πt ] cos [(252+250)πt ]

(d) y = 100 cos (100πt + 0.5x)

During propagation of a plane progressive mechanical wave

A 2 m-long string fixed at both ends is set into vibrations in its first overtone. The wave speed on the string is 200 m s⁻¹ and amplitude is 05 cm. (A) Find the wavelength and the frequency. (B) Write the equation giving the displacement of different points as a function of time. Choose the X-axis along the string with the origin at one end and t = 0 at the instant when the point x = 50 cm has reached its maximum displacement.

The transverse displacement of a string (clamped at its both ends) is given by:

All the points on the string between two consecutive nodes vibrate with

A transverse harmonic wave on a string is described by Where x and y are in cm and t is in s. The positive direction of x is from left to right.

Two successive resonance frequencies in an open organ pipe are 1944 Hz and 2592 Hz. Find the length of the tube. The speed of sound in air is 324 m s^-1.

The displacement of a string is given by Where and are in m and t in s. The length of the string is 1.5m and its mass is.

Find the change in the volume of 1.0 liter kerosene when it is subjected to an extra pressure of 2.0 × 10⁵ N m^-2 from the following data. Density of kerosene = 800 kg m^-3 and speed of sound in kerosene 1330 m s^-1.