Home
Class 11
PHYSICS
Show that when a string fixed at its two...

Show that when a string fixed at its two ends vibrates in 1 loops, 2 loops , 3 loops and 4 loops , the frequencies are in the ratio `1:2:3:4.`

Text Solution

Verified by Experts

Let there are n number of loops in the string.

Length corresponding each loop is `(lambda)/(2)`
Now, we can write
`" " L=(nlambda)/(2)rArrlambda=(2L)/(n)" "` [ for n loops ]
`rArr" (v)/(v)=(2L)/(n)rArr[ :. v=vlambda]`
`rArr" " v=(n)/(2L)v=(n)/(2L)sqrt((T)/(mu))" " [ :.` velocity of transverse waves =`sqrt(T//mu )`]
`rArrvpropn" " ` [ `:.` length and speed are constants ]
So, `" " v_(1):v_(2):v_(3):v_(4)=n_(1):n_(2):n_(3):n_(4)`
`" "=1:2:3:4`
Promotional Banner

Topper's Solved these Questions

  • WAVES

    NCERT EXEMPLAR|Exercise LONG ANSWER TYPE QUESTIONS|5 Videos

  • WAVES

    NCERT EXEMPLAR|Exercise VERY SHORT ANSWER TYPE QUESTIONS|7 Videos

  • UNITS AND MEASUREMENTS

    NCERT EXEMPLAR|Exercise Long Answer Type Questions|9 Videos

  • WORK, ENERGY AND POWER

    NCERT EXEMPLAR|Exercise Long answer|1 Videos

Similar Questions

Explore conceptually related problems

Show that when a string fixed at its two ends vibrates in 1 loops, 2 loops , 3 loops and 4 loops , the frequencies are in the ration 1:2:3:4.

When a string fixed at its both ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequencies are in the ratio

A string fixed at its both ends vibrates in 5 loops as shown in the figure

If a string fixed at both ends vibrates in four loops. The wavelength is 10 cm. The length of string is

A string is vibrating in n loops. The numbers of nodes and anitnodes respectively are

Standing wavs are produced in a stretched string of length 8 m. If the string vibrates in 4 loops and the wave velocity is 20 m/s, then the frequency of the string will be

Four standing wave segments, or loops, are observed on a string fixed at both ends as it vibrates at a frequency of 140 Hz. What is the fundamental frequency of the string?

Two circular loops A and B of radii R and 4R are kept concentrically in the same plane. The loops carry currents I_(1) and I_(2) respectively. If the magnetic field at a point on the common axis of the loops at a distance 2R from their common centre is zero, the ratio (I_(1))/(I_(2)) is _________.