A transverse mechanical wave is traveling along a string lying along the x-axis.

Question

A transverse mechanical wave is traveling along a string lying along the x-axis. The displacement of the string as a function of position and time, y(x,t), is described by the following equation:

where x and y are in meters and the time is in seconds

A) What is the wavelength of the wave?

B) What is the velocity of the wave? (Define positive velocity along the positive x-axis.)

C) What is the maximum speed in the y-direction of any piece of the string? (Give a positive answer for speed.)

Explanation / Answer

here,

y(x,t) = 0.038 * sin(6 * x - 122 t) ..(1)

A)

equivalent equation , y(x,t) = A sin (2*pi*x/lamda - t * 2 * pi* t/T)

on compairibng these equations

2 * pi /lamda = 6

lamda = 1.05 m

the wavelength of the wave is 1.05 m

B)

differentiating equation (1) with respect to t

v(x,t) = 0.038 * 122 * sin(6 * x - 122 t)

v(x,t) = - 4.64* sin(6 * x - 122 t)

the velocity of the wave is , v(x,t) = - 4.64* sin(6 * x - 122 t)

(C)

the maximum value of sin() function is 1

therefore , the maximum speed , vmax = 4.64 m/s

the maximum speed in the y-direction of any piece of the string is 4.64 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.