Assignment-4
Q-1. A sinusoidal wave travels along a string. The time for a particular point to
move from maximum displacement to zero is 0.170 s. What are the (a) period and
(b) frequency? (c) The wavelength is 1.40 m; what is the wave speed?
Q-2. A transverse sinusoidal wave is moving along a string in the positive direction
of an x axis with a speed of 80 m/s. At t = 0, the string particle at x = 0 has a
transverse displacement of 4.0 cm from its equilibrium position and is not moving.
The maximum transverse speed of the string particle at x = 0 is 16 m/s. (a) What is
the frequency of the wave? (b) What is the wavelength of the wave? If
𝑦(𝑥, 𝑡) = 𝑦 sin(𝑘𝑥 ± 𝜔𝑡 + ∅)
is the form of the wave equation, what are (c) ym, (d) k, (e) 𝜔, (f) ∅, and (g) the
correct choice of sign in front of 𝜔?
Q-3. A sinusoidal wave moving along a string is shown twice in figure, as crest A
travels in the positive direction of an x axis by distance d = 6.0 cm in 4.0 ms. The
tick marks along the axis are separated by 10 cm; height H = 6.00 mm. The
equation
for the wave is in the form
𝑦 = 𝑦 sin(𝑘𝑤 ± 𝜔𝑡)
so what are (a) 𝑦 , (b) k, (c) 𝜔, and (d) the correct choice of sign in front of 𝜔?
Q-4. The equation of a transverse wave traveling along a very long string is
𝑦 = 0.6 sin(0.020𝜋𝑥 + 4.0𝜋𝑡)
where x and y are expressed in centimeters and t is in seconds. Determine (a) the
amplitude, (b) the wavelength, (c) the frequency, (d) the speed, (e) the direction of
propagation of the wave, and (f) the maximum transverse speed of a particle in the
string. (g) What is the transverse displacement at x = 3.5 cm when t = 0.26 s?
Q-5. The equation of a transverse wave on a string is
𝑦 = (2.0𝑚𝑚) sin(20𝑚 𝑥 − 600𝑠
𝑡)
Tension in the string is 15 N. (a) What is the wave speed? (b) Find the linear
density of this string in grams per meter.
Q-6. A 100 g wire is held under a tension of 250 N with one end at x = 0 and the
other at x = 10.0 m. At time t = 0, pulse 1 is sent along the wire from the end at x =
10.0 m. At time t = 30.0 ms, pulse 2 is sent along the wire from the end at x = 0. At
what position x do the pulses begin to meet?
Q-7. Two identical traveling waves, moving in the same direction, are out of phase
by 𝜋/2 rad. What is the amplitude of the resultant wave in terms of the common
amplitude ym of the two combining waves?
Q-8. What phase difference between two identical traveling waves, moving in the
same direction along a stretched string, results in the combined wave having an
amplitude 1.50 times that of the common amplitude of the two combining waves?
Express your answer in (a) degrees, (b) radians, and (c) wavelengths.
Q-9 A harmonic plane wave in a water pond is moving in a particular direction that
we can call x-axis. The wave has an amplitude of 0.5 m and a wavelength of 0.25
m whereas its speed is 2 m/s. What is the angular frequency and angular wave
number of this wave? How many waves fit in a length of 10 m. Suppose at t = 0
there is a full peak at x = 0. What is the height of water at x = 2 m and x = 2.1 m at
this time? What is the height at these same points at t = 1 s?
Q-10Consider two waves that are superposing
What is the wavelength of the resultant wave? What is the amplitude of the
resultant wave?