Question: A string of length 2.0 meters is fixed at both ends and has a tension of 50 N. A student creates standing waves on the string by oscillating one end at a frequency of 100 Hz. If two adjacent nodes are 40 cm apart on the string, calculate the speed of the waves on the string.

Answer: To find the speed of the waves on the string, we can use the formula: [ v = f \lambda ] Where: $v$ = speed of the waves $f$ = frequency of the waves $\lambda$ = wavelength of the waves

First, let's calculate the wavelength using the given distance between two adjacent nodes (40 cm): $\lambda = 2L/n$ Where: $L$ = length of the string $n$ = number of segments between the nodes

Since there are two adjacent nodes, there is one segment between them. So, $n = 1$.

$\lambda = 2(2.0) / 1 = 4.0 \,m$

Now, we can use the formula to solve for the speed of the waves: $v = (100 \,Hz) \times (4.0 \,m)$ $v = 400 \,m/s$

Therefore, the speed of the waves on the string is 400 m/s.