Chapter 15: Waves

A transverse harmonic wave on a string is described by y (x,t) = 3.0 sin (36t + 0.018x + π/4) where x and y are in cm and t is in s. The positive direction of x is from left to right

a) the wave is travelling from right to left

b) the speed of the wave is 20 m/s

c) frequency of the wave is 5.7 Hz

d) the least distance between two successive crests in the wave is 2.5 cm

The displacement of a string is given by y(x,t) = 0.06 sin (2πx/3) cos (120πt) 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^-2kg.

a) it represents a progressive wave of frequency 60 Hz

b) it represents a stationary wave of frequency 60 Hz

c) it is the result of the superposition of two waves of wavelength 3 m, frequency 60 Hz each travelling with a speed of 180 m/s in the opposite direction

d) amplitude of this wave is constant

Speed of sound waves in a fluid depends upon

a) directly on the density of the medium

b) square of bulk modulus of the medium

c) inversely on the square root of density

d) directly on the square root of bulk modulus of the medium

During propagation of a plane progressive mechanical wave

a) all the particles are vibrating in the same phase

b) amplitude of all the particles is equal

c) particles of the medium executes SHM

d) wave velocity depends upon the nature of the medium

The transverse displacement of a string is given by y(x,t) = 0.06 sin (2πx/3) cos (120πt). All the points on the string between two consecutive nodes vibrate with

a) same frequency

b) same phase

c) same energy

d) different amplitude

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. Given that the speed of sound in still air is 340 m/s

a) the frequency of sound as heard by an observer standing on the platform is 400 Hz

b) the speed of sound for the observer standing on the platform is 350 m/s

c) the frequency of sound as heard by the observer standing on the platform will increase

d) the frequency of sound as heard by the observer standing on the platform will decrease

Which of the following statements is true for a stationary wave?

e) there are some particles which are always at rest

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

An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork?

A tuning fork A, marked 512 Hz, produces 5 beats per second, where sounded with another unmarked tuning fork B. If B is loaded with wax, the number of beats is again 5 per second. What is the frequency of the tuning fork B when not loaded?