Standing waves on string

1. Waves

2. A vibrator produces waves in a string, whose
L=2.0 meters and is connected to a
blackboard as shown below.

3. A. Draw the waves as it reaches the
blackboard and after it touches it. Also
determine the direction of the waves
and label the node and the antinode.
(The standing wave
that is produced is 4th
Harmonic.)

4. B. The time taken to complete 1 round,
that is ends where it started, is 0.45
seconds.
 What is wave’s frequency?
 How fast does the wave travel?
Solution:
4 complete cycles are covered by the wave as it travels a round.
f = 4 cycles = 8.89 Hz
0.45 s
The wavelength if 1.0 m.
v = fλ = (8.89 Hz)(1.0 m) = 8.89 m/s

5. C. The situation remains the same,
however, the tension is reduced to 3 N.
The linear density is 0.09 kg/m.
 Calculate the string’s wave speed .
 Also, calculate the wavelength of the wave.
Solution:
v = √(Ts/μ) = √(3 N/ 0.09 kg/m) = 5.77 m/s
λ = v/f = (5.77 m/s) / (8.89 Hz) = 0.649 m

6. D. Now the tension of the string is
increased even more than at the
beginning of the situation.
 Describe the difference in the wavelength from part A.
Explain.
 Sketch the wave with increased tension.
Solution:
The wave speed increases with increasing tension. Frequency reflects no change.
Wavelength is proportional to wave speed, therefore, the wavelength increases.