Final answer:
The student's question involves calculating the wave speed on a string, which is determined by the string's tension and linear mass density, and how this speed affects the frequency and wavelength of standing waves.
Step-by-step explanation:
The student's question relates to the speed of transverse waves on a string under tension and the relationship of this speed to the properties of the string such as tension, linear mass density, and the resulting wave frequency and wavelength. To find the speed of the wave on a string, we use the formula v = √(T/μ), where v is the wave speed, T is the tension, and μ (mu) represents the linear mass density of the string. For instance, in the case of the guitar string, the linear mass density is calculated using μ = (ρ * π * r^2) where ρ is the density of the material, π is the constant Pi, and r is the radius of the string.
To calculate the wave speed on a piano wire or guitar string, the same principle applies, considering both the given linear mass density and tension. Adjusting the tension will affect the wave speed, which in turn determines the frequency and wavelength of the standing waves that are produced when the string vibrates. For example, the tension necessary for the low E string on a guitar to have the same wave speed as the high E string would be much higher due to its greater linear mass density.