Question

Huhuhu. :'( Help me physics a level in high school.​ Thank you

Answer 1

Question:-

When plucked, a 0.62 m guitar string produces a sound wave with a fundamental frequency of 196 Hz. The speed of sound in air is 343 m/s. Determine the ratio of the wavelength of the sound wave to the wavelength of the waves that travel on the string.

Answer:-

$\red{\bigstar}$ Ratio of wavelengths $\large\leadsto\boxed{\rm\purple{Option. D \rightarrow 1.4}}$

• Given:-

Length of guitar string = 0.62 m

Frequency of sound wave = 196 Hz

Speed of sound in air = 343 m/s

• Solution:-

We know,

Wavelength of the sound in air:-

$\large\boxed{\pink{\bf v = f \times \lambda}}$

here,

v = Speed of sound in air

f = frequency of sound wave

λ = wavelength of sound wave

Hence,

➙ $\sf 343 = 196 \times \lambda$

➙ $\sf \lambda = \dfrac{343}{196}$

➙ $\green{\bf \lambda = 1.75}$

Now,

Wavelength of the sound on the string:-

The fundamental frequency [f] on a string fixed at both ends (like guitar string) is such that the length of the string is λ/2.

So ,

λ = 2 × L

➙ $\sf \lambda = 2 \times 0.62$

➙ $\green{\bf \lambda = 1.24}$

Therefore,

Ratio of wavelength of the sound wave to the wavelength of the waves that travel on string:-

➙ $\sf \dfrac{1.75}{1.24}$

➙ $\large\red{\bf 1.4}$