Question

Transverse waves are sent along a 4.50 m long string with a speed of 85.00 m/s. The string is under a tension of 20.00 N. What is the mass of the string (in kg)?

Answer 1

Answer:

m = 0.0125 kg

Explanation:

Let us apply the formula for the speed of a wave on a string that is under tension:

$v = \sqrt{\frac{F}{\mu} }$

where F = tension force

μ = mass per unit length

Mass per unit length is given as:

μ  = m / l

where m = mass of the string

l = length of the string

This implies that:

$v = \sqrt{\frac{F}{m/l} }\\ \\v = \sqrt{\frac{F * l}{m} }$

Let us make mass, m, the subject of the formula:

$v^2 = \frac{F * l}{m}\\\\m = \frac{F * l}{v^2}$

From the question:

F = 20 N

l = 4.50 m

v = 85 m/s

Therefore:

$m = \frac{20 * 4.5}{85^2}\\\\m = \frac{90}{7225}\\ \\m = 0.0125 kg$