Wavelength of traveling wave on string (one end clamped and one end free)

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  • #1
Dalip Saini
16
0
1. Homework Statement
A 30-cm long string, with one end clamped and the other free to move transversely, is vibrating in its second harmonic. The wavelength of the constituent traveling waves is
  • A -- 10 cm
  • B -- 40 cm
  • C -- 120 cm
  • D -- 30 cm
  • E -- 60 cm

Homework Equations


for second harmonic n=2
(2L)/n= wavelength

The Attempt at a Solution


(2*30)/(2) = 30 cm
Put the answer is 40 cm, and I don't understand why
 
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  • #2
Dalip Saini said:

Homework Statement


A 30-cm long string, with one end clamped and the other free to move transversely, is vibrating in its second harmonic. The wavelength of the constituent traveling waves is

Homework Equations


for second harmonic n=2
(2L)/n= wavelength

The Attempt at a Solution


(2*30)/(2) = 30 cm
Put the answer is 40 cm, and I don't understand why

The formula you used is wrong. Where are the nodes and antinodes of that vibrating spring?
 
  • #3
To expand on ehild's answer, you have used the expression for a string where both ends are fixed (or both free). You need to correct forthe fact that your string is fixed in one end and free in the other. This goes for both your threads.
 
  • #4
Dalip Saini said:
1. Homework Statement
A 30-cm long string, with one end clamped and the other free to move transversely, is vibrating in its second harmonic. The wavelength of the constituent traveling waves is
  • A -- 10 cm
  • B -- 40 cm
  • C -- 120 cm
  • D -- 30 cm
  • E -- 60 cm

Homework Equations


for second harmonic n=2
(2L)/n= wavelength

The Attempt at a Solution


(2*30)/(2) = 30 cm
Put the answer is 40 cm, and I don't understand why
in terms of waves clamped at one end we use the formula 'amplitude=4L/n', however the trick is that their number of harmonics can only be an odd number (1,3,5,7 etc) so the second harmonic must be n=3. by substituting that of the above formula you will get 40 cm. The key words were 'clamp at one end than 2 ends.' for strings clamped at 2 end we use 'amplitude=2L/n' and n can either be an odd or even number.
 

1. What is the formula for calculating the wavelength of a traveling wave on a string with one end clamped and one end free?

The formula for calculating the wavelength of a traveling wave on a string with one end clamped and one end free is λ = 2L/n, where λ is the wavelength, L is the length of the string, and n is the number of segments or nodes in the standing wave.

2. How does the tension of the string affect the wavelength of the traveling wave?

The tension of the string affects the wavelength of the traveling wave by increasing it. As the tension increases, the speed of the wave also increases, resulting in a longer wavelength. This is because the wavelength is directly proportional to the speed of the wave, which is determined by the tension and mass per unit length of the string.

3. Can the wavelength of a traveling wave on a string with one end clamped and one end free be changed?

Yes, the wavelength of a traveling wave on a string with one end clamped and one end free can be changed by adjusting the length of the string or the tension applied to it. Increasing the length or tension will result in a longer wavelength, while decreasing them will result in a shorter wavelength.

4. What is the relationship between the wavelength and frequency of a traveling wave on a string?

The wavelength and frequency of a traveling wave on a string have an inverse relationship. This means that as the wavelength increases, the frequency decreases, and vice versa. This relationship is described by the equation v = fλ, where v is the velocity of the wave, f is the frequency, and λ is the wavelength.

5. How does the density of the string affect the wavelength of the traveling wave?

The density of the string affects the wavelength of the traveling wave by decreasing it. As the density increases, the speed of the wave decreases, resulting in a shorter wavelength. This is because the wavelength is inversely proportional to the speed of the wave, which is determined by the density and tension of the string.

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