PHYSICS HIGH SCHOOL

A cellist tunes the C string of her instrument to a fundamental frequency of 65.4 Hz . The vibrating portion of the string is 0.600 m long and has a mass of 14.4 g .What is μ, the mass per unit length of the string?
To determine the wave speed from purely kinematic quantities, you need to know the wavelength of the wave. What is the wavelength λ of the fundamental mode in the C string of the cello?

Answers

Answer 1

Answer:

Explanation:

Given that,

Fundamental frequency of the string, f = 65.4 Hz

Length of the string, l = 0.6 m

Mass, m = 14.4 g = 0.0144 kg

(a) Let $\mu$ is the mass per unit length of the string. It can be calculated as :

$\mu=(m)/(l)$

$\mu=(0.0144\ kg)/(0.6\ m)$

$\mu=0.024\ kg/m$

(b) If f is the fundamental frequency of the string, the wavelength of the fundamental mode is given by :

$l=(n\lambda)/(2)$

$\lambda=(2l)/(n)$

n = 1

$\lambda=2l=2* 0.6\ m$

$\lambda=1.2\ m$

Hence, this is the required solution.

Answer 2

Answer:

The mass per unit length of the string is 0.024 kg/m, and the wavelength is 1.2 meters.

What is the frequency?

It is defined as the number of waves that crosses a fixed point in one second known as frequency. The unit of frequency is per second.

We have:

Fundamental frequency = 65.4 Hz

Length of the vibrating string portion = 0.6 meter

Mass of the vibrating string portion = 144 grams

We know the formula for mass per unit length:

$\rm \mu = (m)/(l)$

$=\rm (0.0144 \ kg)/(0.6 \ meter)$ ( m = 144 grams ⇒ 0.0144 kg)

$\rm \mu = 0.024 \ kg/m$

The wavelength of the fundamental mode is given by:

$\rm l =(n\lambda)/(2)$

$\rm \lambda = (2l)/(n)$

$\rm \lambda = 2* 0.6 \Rightarrow 1.2 meter$ (n = 1)

Thus, the mass per unit length of the string is 0.024 kg/m, and the wavelength is 1.2 meters.

Learn more about the frequency here:

brainly.com/question/27063800

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