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

[Dalip Saini]

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

 

[ehild]

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?

 

[Orodruin]

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.

 

[Ms Khoza]

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.