In a transverse wave on a stretched string, the wavelength is $\lambda =0.80m$ and the frequency is $f=5.0\mathrm{Hz}$. What is the wave speed?

• A. $v=\frac{\lambda }{f}=0.16m·s$
• B. $v=f+\lambda =5.8$
• C. $v=f\lambda =4.0m/s$
• D. $v=\frac{f}{\lambda }=6.25s-1$

Answer: (C)

Verified step by step guidance

1. Identify the given quantities: the wavelength \(\lambda = 0.80\ \text{m}\) and the frequency \(f = 5.0\ \text{Hz}\).
2. Recall the fundamental relationship between wave speed \(v\), frequency \(f\), and wavelength \(\lambda\): \[v = f \times \lambda\]
3. Substitute the known values into the formula: \[v = 5.0 \times 0.80\]
4. Perform the multiplication to find the wave speed (do not calculate the final number here, just set up the expression).
5. Express the wave speed with the correct units, which are meters per second (\(\text{m/s}\)).