Wave Speed on a Stretched String (Edexcel A Level Physics): Revision Note

A guitar string of mass 3.2 g and length 90 cm is fixed onto a guitar.

The string is tightened to a tension of 65 N between two bridges at a distance of 75 cm.

Calculate the

a) speed of the waves on the string

b) fundamental frequency of the string

Answer:

Part (a)

Step 1: Write the known quantities in S.I. units

• Tension, T = 65 N

• Mass, m = 3.2 g = 3.2 × 10⁻³ kg

• Length of string, L = 90 cm = 0.90 m

  • Mass per unit length, μ = $\frac{m}{L}=\frac{3.2\times {10}^{-3}}{0.9}$ = 3.56 × 10⁻³ kg m⁻¹

Step 2: Write the equation for speed on a string and calculate

• v = fλ = f × 2L AND f = $\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

• So, v = $\frac{1}{2L}\sqrt{\frac{T}{\mu }}\times 2L=\sqrt{\frac{T}{\mu }}$

$v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{65}{3.56\times {10}^{-3}}}$ = 135

Step 3: Write the answer to the correct significant figures and include units

• The speed of the wave on the string, v = 140 m s⁻¹

Part (b)

Step 1: Write the known quantities in S.I. units

• Tension, T = 65 N

• Length of string under tension, L = 75 cm = 0.75 m

• Mass per unit length, μ = 3.56 × 10⁻³ kg m⁻¹ (from part (a))

Step 2: Identify the length of one wavelength at the fundamental frequency, f₀

Step 3: Write the equation for fundamental frequency and calculate

$f_0=\frac{1}{2L}\sqrt{\frac{T}{\mu }}=\frac{v}{2L}=\frac{135}{(2\times 0.75)}$ = 90.1

Step 3: Write the answer to the correct significant figures and include units

• The fundamental frequency, f₀ = 90 Hz

Go through solutions step by step, showing all your working. Questions like this one will be very similar so you can rely on using your tried and tested method to get the answer.