Watch the following video and answer the following questions. For the sixth harm
ID: 1588098 • Letter: W
Question
Watch the following video and answer the following questions. For the sixth harmonic how many wavelength and nodes and anti-nodes can you identify The speed of the wave traveling in the rope can be determined via v=f lambda, where f is the frequency of the wave generated by the signal generator. Listen carefully to the demonstrator to see what frequency is applied. Having the frequency and the length of the rope 150 cm, determine the speed of the wave in the rope (Part 2 of the video can be helpful to calculate the needed quantity)Explanation / Answer
Part (a)
Nodes are said to be present where the rope has zero displacement and anti-nodes occur where the rope has maximum displacement.
From the video, for the sixth harmonic we can identify, we can observe three complete wavelengths along the length of the rope, 7 nodes (two fixed nodes at the both ends plus five nodes in between) and 6 antinodes. Thus the answer to this part is,
Wavelength = 3
Nodes = 7
Antinodes = 6
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Part (b) Length of the rope, L = 150 cm
From the 1st video, we note that the fundamental frequency (which is needed for the first harmonic) is f1 = 8.5 Hz.
Thus frequency needed for sixth harmonic is six times the fundamental frequency, f6 = 6*8.5 Hz = 51 Hz
At the six harmonic, the whole length of string contains three wavelength,
L = 3*
= L/3
= (150 cm)/3
= 50 cm
Thus from the given equation, the speed of the wave v,
v = f6*
v = (51 Hz)*(50cm)
v = (51/s)*(50cm) (1 Hz = 1/sec)
v = 2550 cm/s
Thus the answer is,
Speed of wave is 2550 cm/s.
[ The same result as above can be obtained by considering the fundamental frequency, f1= 8.5 Hz.
At the fundamental frequency, the whole length of rope contains half the wavelength
/2 = L
/2 = 150 cm
= 300 cm
Thus the speed of wave is,
v = f1*
v = (8.5 Hz)*(300cm)
v = 2550 cm/s ]
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