Wave Speed on a Stretched Spring (Edexcel International A Level Physics)

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 =  = 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 = 

• So, v =

= 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

= 90.1

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

• The fundamental frequency, f₀ = 90 Hz

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