Question

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?

                                             

Solution

Correct option is

0.2 m

 

Path difference for two consecutive maxima = λ, i.e.

                        

.  

Also BQ = 2.4 m.   

Thus  2.6 – 2.4 = λ or λ = 0.2 m.

SIMILAR QUESTIONS

Q1

A sonometer wire, with a suspended mass of M = 1 kg, is in resonance with a given tuning fork. The apparatus is taken to the moon where the acceleration due to gravity is 1/6 that on earth. To obtain resonance on the moon, the value of M should be

Q2

A source of sound vibrates according to the equation y = 0.05 cos π t. It sends waves of velocity 1.5 ms –1. The wavelength of the waves is    

Q3

Two identical waves, each of frequency 10 Hz, are travelling in opposite directions in a medium with a speed of 20 cm s–1. The distance between adjacent nodes is

Q4

Figure shows the shape of part of a long string in which transverse waves are produced by attaching one end of the string to tuning fork of frequency 250 Hz. What is the velocity of the waves?

                                                  

Q5

 

Particle displacements (in cm) in a standing wave are given by 

                     

The distance between a node and the next anti-node is

Q6

If Young’s modulus of the material of a rod is  and its density is 8000 kg m–3, the time taken by a sound wave to traverse 1 m of the rod will be 

Q7

An observer moves towards a stationary source of sound with a velocity one-tenth the velocity of sound. The apparent increase in frequency is

Q8

A stone hangs from the free end of a sonometer wire whose vibrating length, when tuned to a tuning fork, is 40 cm. When the stone hangs wholly immersed in water, the resonant length is reduced to 30 cm. The relative density of the stone is

Q9

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Q10

 

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