Question

Three waves of equal frequency having amplitude 10 μm, 4 μm and 7μ arrive at a given point with a successive phase difference of π/2. The amplitude of the resulting wave in μ m is given by

Solution

Correct option is

5

 

The amplitude of the three waves are a1 = 10 μm, a2 = 4 μm and a3 = 7 μm. Let the phase of the first wave be zero. Then the wave of the second wave = π/2 and of third wave  Therefore, the phase difference between the first wave and third wave is π. Hence their resultant is 

                        

The phase difference between this resultant (of first and third waves) and the second wave = π/2. Therefore, the resultant of a and a3 is

                        

SIMILAR QUESTIONS

Q1

The speed of sound in hydrogen at STP is v. The speed of sound in a mixture containing 3 parts of hydrogen and 2 parts of oxygen at STP will be 

Q2

The speed of sound in hydrogen at STP is v. What is the speed of sound in helium at STP?

Q3

Nine tuning forks are arranged in order of increasing frequency. Each tuning fork produces 4 beats per second when sounded with either of its neighbours. If the frequency of the 9th tuning fork is twice that of the first, what is the frequency of the first tuning fork?

Q4

A sonometer wire of length 120 cm is divided into three segments of lengths in the ratio of 1: 2: 3. What is the ratio of their fundamental frequencies?

Q5

A tuning fork produces 4 beats per second when sounded with a sonometer of vibrating length 48 cm. It produces 4 beats per second also when the vibrating length is 50 cm. What is the frequency of the tuning fork?

Q6

Two identical strings of a stringed musical instrument are in unison when stretched with the same tension. When the tension in one string is increased by 1%, the musician hears 4 beats per second. What was the frequency of the note when the strings were in unison?

Q7

Two identical flutes produce fundamental notes of frequency 300 Hz at 27oC. If the temperature of the air in one flute is increased to 31oC, the number of beats heard per second will be

Q8

The wavelength of light of a particular wavelength received from a galaxy is measured on earth and is found to be 5% more that its wavelength. It follows that the galaxy is

Q9

Radio waves of frequency 600 MHz are sent by a radar towards an enemy aircraft. The frequency of the radio waves reflected from the aircraft as measured at the radar station is found to increase by 6 kHz. It follows that the aircraft is

Q10

Two wires of the same material and radii r and 2r are welded together end to end. The combination is used as a sonometer wire and kept under tension T. The welded point is mid-way between the two bridges. When stationary waves are set up in the composite wire, the joint is a node. Then the ratio of the number of loops formed in the thinner to thicker wire is