Advertisements
Advertisements
Question
The length of the wire shown in figure between the pulley is 1⋅5 m and its mass is 12⋅0 g. Find the frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest.
Advertisements
Solution
Given:
Length of the wire between two pulleys (L) = 1.5 m
Mass of the wire = 12 gm
\[\text{ Mass per unit length,} m = \frac{12}{1 . 5} g/m\]
\[ = 8 \times {10}^{- 3} kg/m\]
\[Tension in the wire, T = 9 \times g\]
\[ = 90 \text{ N }\]
Fundamental frequency is given by:
\[f_0 = \frac{1}{2L} \sqrt{\left( \frac{T}{m} \right)}\]
For second harmonic (when two loops are produced):
\[f_1 = 2 f_0 = \frac{1}{1 . 5} \sqrt{\left( \frac{90}{8} \times {10}^{- 3} \right)}\]
\[ = \frac{\left( 106 . 06 \right)}{1 . 5}\]
\[ = 70 . 7 Hz \approx 70 Hz\]
APPEARS IN
RELATED QUESTIONS
A wave is represented by an equation \[y = c_1 \sin \left( c_2 x + c_3 t \right)\] In which direction is the wave going? Assume that \[c_1 , c_2\] \[c_3\] are all positive.
What is the smallest positive phase constant which is equivalent to 7⋅5 π?
If you are walking on the moon, can you hear the sound of stones cracking behind you? Can you hear the sound of your own footsteps?
The voice of a person, who has inhaled helium, has a remarkably high pitch. Explain on the basis of resonant vibration of vocal cord filled with air and with helium.
When we clap our hands, the sound produced is best described by Here p denotes the change in pressure from the equilibrium value.
When two waves with same frequency and constant phase difference interfere,
A man stands before a large wall at a distance of 50.0 m and claps his hands at regular intervals. Initially, the interval is large. He gradually reduces the interval and fixes it at a value when the echo of a clap merges every 3 seconds, find the velocity of sound in air.
Two point sources of sound are kept at a separation of 10 cm. They vibrate in phase to produce waves of wavelength 5.0 cm. What would be the phase difference between the two waves arriving at a point 20 cm from one source (a) on the line joining the sources and (b) on the perpendicular bisector of the line joining the sources?
A string, fixed at both ends, vibrates in a resonant mode with a separation of 2⋅0 cm between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to 1⋅6 cm. Find the length of the string.
If the sound level in a room is increased from 50 dB to 60 dB, by what factor is the pressure amplitude increased?
A source of sound with adjustable frequency produces 2 beats per second with a tuning fork when its frequency is either 476 Hz of 480 Hz. What is the frequency of the tuning fork?
A piano wire A vibrates at a fundamental frequency of 600 Hz. A second identical wire Bproduces 6 beats per second with it when the tension in A is slightly increased. Find the the ratio of the tension in A to the tension in B.
A boy riding on his bike is going towards east at a speed of 4√2 m s−1. At a certain point he produces a sound pulse of frequency 1650 Hz that travels in air at a speed of 334 m s−1. A second boy stands on the ground 45° south of east from his. Find the frequency of the pulse as received by the second boy.
A train running at 108 km h−1 towards east whistles at a dominant frequency of 500 Hz. Speed of sound in air is 340 m/s. What frequency will a passenger sitting near the open window hear? (b) What frequency will a person standing near the track hear whom the train has just passed? (c) A wind starts blowing towards east at a speed of 36 km h−1. Calculate the frequencies heard by the passenger in the train and by the person standing near the track.
A person standing on a road sends a sound signal to the driver of a car going away from him at a speed of 72 km h−1. The signal travelling at 330 m s−1 in air and having a frequency of 1600 Hz gets reflected from the body of the car and returns. Find the frequency of the reflected signal as heard by the person.
A car moves with a speed of 54 km h−1 towards a cliff. The horn of the car emits sound of frequency 400 Hz at a speed of 335 m s−1. (a) Find the wavelength of the sound emitted by the horn in front of the car. (b) Find the wavelength of the wave reflected from the cliff. (c) What frequency does a person sitting in the car hear for the reflected sound wave? (d) How many beats does he hear in 10 seconds between the sound coming directly from the horn and that coming after the reflection?
For the propagation of longitudinal waves, the medium must have
- elasticity
- mass
- inertia
- force of cohesion
Equation of a plane progressive wave is given by `y = 0.6 sin 2π (t - x/2)`. On reflection from a denser medium its amplitude becomes 2/3 of the amplitude of the incident wave. The equation of the reflected wave is ______.
