Question

A guitar string is fixed at both ends. If you tighten it to increase its tension, the frequencies of its normal modes will increase but its wavelengths will not be affected.

A. True
B. False

Answer 1

The statement is false because while increasing tension raises the frequencies of a guitar string's normal modes, the wavelengths remain constant as they are determined by the fixed length of the string.

Step-by-step explanation:

The statement given is False. When you tighten a guitar string, thus increasing its tension, this alters the speed of waves on the string. According to the formula for the fundamental frequency (f1 = vw/2L), where vw is the wave speed, L is the length of the string, and λ1 is the wavelength corresponding to the fundamental frequency, the frequency indeed increases. However, since the string is still fixed at both ends, the wavelengths of the standing waves, which are determined by the length of the string and the boundary conditions, do not change. The harmonic frequencies are calculated as f2 = vw/L = 2f1, f3 = 3f1, and so on, indicating that they are integer multiples of the fundamental frequency.

Increasing the tension has no effect on the length of the string; thus, although the frequencies of the normal modes will increase, the wavelengths will remain constant because they are directly related to the physical length of the string, which does not change.

Answer 2

Answer:True

Step-by-step explanation:

We know that frequency in a tight string is given by

`\\u =\sqrt{(T)/(\mu )}`

where
`\\u =Frequency\ of\ sound\ waves`

`T=Tension`

`\mu =mass\ per\ unit\ length`

and velocity is given by

`v=\\u \lambda`

As
`\\u` increases v also increase but wavelength
`(\lambda)` remain same because ends of string are fixed.