A cello string vibrates in its fundamental node with a frequency of 220 Hz. The string's vibrating length is 49.2 cm.

Question

(A) Find the speed of the wave on this string. __________

(B) Find the frequency of this string when it vibrates with 6 nodes and 5 anti-nodes. __________

Answer 1

1) you are given frequency. Wavelength/2 = Length for fundamental. Therefore wavelength is 2L

You know that v = (f)(λ) or cycle/s * cm/cycle = cm/s

2) With 5 antinodes, you have 5 half wavelengths, so 5/2 λ = L (solve for λ)

f for this standing wave is v from part (1) divided by new λ

or you can use the fact that this is the fifth harmonic so f₅ = 5f₁