If the tension doubles on a string, the wave speed v on that string will increase by what factor (approximately)?

If the tension doubles on a string, the wave speed v on that string will increase by what factor (approximately)?

• A. sqrt(2)
• B. 2
• C. 1/2
• D. 1

Answer: (A)

The main idea is that waves on a string move at a speed that depends on tension and how much mass is in the string per length. The relationship is v = sqrt(T/μ), where μ is the linear mass density. If the tension doubles while μ stays the same, the new speed is v' = sqrt(2T/μ) = sqrt(2) sqrt(T/μ) = sqrt(2) v. So the wave speed increases by a factor of about sqrt(2). This reflects the string getting stiffer, so disturbances propagate faster, but the increase is only with the square root of the tension. (Assumes μ remains unchanged.)

The main idea is that waves on a string move at a speed that depends on tension and how much mass is in the string per length. The relationship is v = sqrt(T/μ), where μ is the linear mass density. If the tension doubles while μ stays the same, the new speed is v' = sqrt(2T/μ) = sqrt(2) sqrt(T/μ) = sqrt(2) v. So the wave speed increases by a factor of about sqrt(2). This reflects the string getting stiffer, so disturbances propagate faster, but the increase is only with the square root of the tension. (Assumes μ remains unchanged.)