wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

One end of a long string of linear mass density 8.0 ×103 kg m1 is connected to an electrically driven tuning fork of frequency 256 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90 kg. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At t = 0, the left end (fork end) of the string x = 0 has zero transverse displacement (y = 0) and is moving along positive y-direction. The amplitude of the wave is 5.0 cm. Write down the transverse displacement y as function of x and t that describes the wave on the string :

Open in App
Solution

The equation of a travelling wave propagating along the positivey-direction is given by the displacement equation:
y(x,t)=asin(wtkx) ...(i)
Linear mass density, μ=8.0×103kgm1
Frequency of the tuning fork, v=256Hz
Amplitude of the wave, a=5.0cm=0.05m ...(ii)
Mass of the pan, m =90kg
Tension in the string, T=mg=909×9.8=882N
The velocity of the transverse wave v, is given by the relation:
v=Tμ
=8828.0×103=332m/s
Angular Frequency, ω=2πf
=2×3.14×256
=1608.5=1.6×103rad/s ...(iii)

Wavelength, λ=vf=332256m
Propagation constant, k=2πλ

=2×3.14332256=4.84m1 ...(iv)
Substituting the values from equations (ii), (iii), and (iv) in equation (i), we get the displacement equation:
y(x,t)=0.05sin(1.6×103t4.84x)m.

flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
What Sound Really Is
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon