A sinusoidal transverse wave travelling on a string is described at t = 2.0 s by

Question

A sinusoidal transverse wave travelling on a string is described at t = 2.0 s by y(x) = 0.10 sin(4pix + (33pi/4)) where x and y are in meters. At the point x = 1.0 m in the string, the displacement as a function of time is given by y(t) = 0.10sin((17pi/4) + 4pit) What are the wavelength and amplitude of the wave? What is the frequency (in Hz) and direction of propagation of the wave? What is the speed of the wave? Write down the full expression for the displacement of the string, y(x, t), at position, x and time, t. Describe a wave whose simulations presence in the string would lead to a standing wave.

Explanation / Answer

given transverse wave y(x) = 0.1 sin (4pix +(33pi/4)------------>1
annd displacement as a function of time is y(t) = 0.10 sin ((17pi/4)+4pit)----------->2

comparing the equation y(x,t) = A sin (kx - wt + phi)
from eq (1), (2)

a) amplidue is A = 0.10 m, k wave number = 2pi/ lambda = 4 pi ==> lambda = 1/2 pi

b) frequency is , angular frequency w = 2pi *f ==> f = w/ 2pi = 4 pi/2 pi = 2 Hz , the wave is propagating in the negative x- direction

c) speed of wave is v = w/k = 2/4pi = 1/2pi = 0.159 m/s

d) y(x,t )= 0.10 sin (4pi x + 2t +5pi)

e) standing waves will be formed if two waves of same frequency and amplide are propagating in the opposite directions then superposition of waves takes place so that

   crest of one wave overlap with crest of the other wave in opposite direction, resulting antinode region and same wave as troughs results node region.which is called standing wave.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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