# Day 3 Waves

```Waves
Assignment 3
1. A harmonic wave travels in a wire with amplitude 1.16 mm, wavelength 1.26 m, and frequency 650 Hz.
What is the speed with which the wave travels?
2. A sound having a frequency of 200 Hz travels through air at 300 m/s. What is the wavelength?
3. A rock dropped into a pond produces a wave that takes 10 s to reach the opposite shore, 20 m away.
When the first ripple reached the shore, there were 5 complete waves formed. What is the frequency of
the wave?
a. What is the speed of the wave on the string?
b. What if the frequency of the fifth harmonic?
5. The 4th harmonic of a standing wave is 20 Hz.
a. Find the fundamental frequency:
b. Find the frequency of the 6th harmonic:
6. A standing wave of frequency 18 hertz is set up on a string 2 meters long with nodes at both ends and in
the center, as shown.
a. Find the speed at which waves propagate on the string.
b. Determine the fundamental frequency of vibration of the string.
c. Which of the following frequencies would NOT produce a standing wave on the string?
A. 27 Hz
B. 36 Hz
C. 60 Hz
D. 81 Hz
7. A student wants to establish a standing wave on a wire 1.8 m long clamped at both ends. The wave
speed is 540 m/s. What is the minimum frequency she should apply to set up standing waves?
8. A stretched string is fixed at both ends, 2.0 m apart. If the density of the string is 1.5 kg/m and its
tension is 600 N. What is the speed of the wave in the string? What is the wavelength of the first
harmonic? What is the frequency of the fourth harmonic?
9. The diagram below shows two waves
traveling in the same medium. Points A, B,
C, and D are located along the rest position
of the medium. The waves interfere to
produce a resultant wave. At which point
will the superposition of the waves produces
the greatest displacement from the rest
position of the medium?
10. Two wires are made of the same material but the second wire has twice the diameter and twice the
length of the first wire. When the two wires are stretched, and the tension in the second wire is also
twice the tension in the first wire, the fundamental frequency of the first wire is 200 Hz. What is the
fundamental frequency of the second wire?
11. Tension is maintained in a 21 m string as in the figure. The observed wave speed is 24 m/s when the
suspended mass is 3.3 kg. What is the wave speed when the suspended mass is 2.2 kg?
12. In the arrangement shown in the figure below, an object of mass 5 kg hangs from a cord around a light
pulley. The length of the cord between point P and the pulley is 2 m. When the vibrator is set to
frequency of 150 Hz, a standing wave with six loops is formed.
a. What must be the linear mass density of the cord?
b. How many complete loops (if any) will result if the mass is changed to 40 kg?
c. How many complete loops (if any) will result if the mass is changed to 45 kg?
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