Question

Solution

Correct option is

0.03 m

Because the rope has a finite mass, the tension in the rope is different at different points on the rope. At the top where the rope is rigidly fixed, the tension = weight of the rope + the weight attached to the free end of the rope = 6 kg + 2 kg = 8 kg wt. Tension at the free end of the rope = 2 kg wt. Since , if the tension becomes 4 times, the frequency is doubled. Since  Hence the wavelength is halved.

SIMILAR QUESTIONS

Q1

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?

Q2

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?

Q3

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?

Q4

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?

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

A tuning fork and a sonometer wire sounded together produce 4 beats per second when the length of the wire is 95 cm or 100 cm. the frequency of the turning fork is