The particle displacements in a travelling harmonic wave are given by 


Where x and y are in centimeters and t is in seconds. What is the phase difference between oscillatory motion at two points separated by a distance of 4 m?


Correct option is



The phase difference ∆ϕ between particles separated by a distance ∆x is given by 


Where λ is the wavelength. Now we know that

                       = coefficient of x in the argument of the sine or cosine function



 since a phase change of 2π, 4π, 6π, etc. Implies no phase change.



A cylindrical tube, open at both ends, has fundamental frequency n. If one of the ends is closed, the fundamental frequency will become


Two loudspeakers A and B, 1.0 m apart, produce sound waves of the same wavelength and in the same phase. A sensitive sound detector, moving along PQ, parallel to line AB, 2.4 m away, detects maximum sound at P (on the perpendicular bisector of AB) another maximum sound when it first reaches Q directly opposite to B, as shown in fig. What is the wavelength of sound emitted by the speakers?




A progressive wave in a medium is represented by the equation 


Where y and x are in cm and t in seconds. The maximum speed of a particle of the medium due to the wave is


A tuning fork of frequency 340 Hz is sounded above a cylindrical tube 1 m high. Water is slowly poured into the tube. If the speed of sound is 340 ms–1, at what levels of water in the tube will the sound of the fork be appreciably intensified? 


A sonometer wire, 65 cm long, is in resonance with a tuning fork of frequency N. If the length of the wire is decreased by 1 cm and it is vibrated with the same tuning fork, 8 beats are heard per second. What is the value of N?


Two organ pipes, each closed at one end, give 5 beats per second when emitting their fundamental notes. If their lengths are in the ratio of 50 : 51, their fundamental frequencies (in Hz) are   


Two sources A and B are sounding notes of frequency 680 Hz. A listener moves from A to B with a constant velocity u. If the speed of sound is 340 ms –1, what must be the value of u so that he hears 10 beats per second?


A hospital uses an ultrasonic scanner of frequency 3.2 MHz to locate tumours in a tissue. What is the wavelength of ultrasonic waves in a tissue in which the speed of the waves is 1.6 km s–1 


A bat flying above a take emits ultrasonic sound of 100 kHz. When this wave falls on the water surface, it is partly reflected and partly transmitted. What are the wavelengths of the reflected and transmitted waves? The speed of sound in air is 340 ms –1 and in water 1450 ms–1


A string of length 10.0 m and mass 1.25 kg is stretched with a tension of 50 N. If a transverse pulse is created at one end of the string, how long does it take to reach the other end?