Physics · Waves · NEET
No. This is the most tested idea. The speed v = sqrt(T/mu) is fixed by the medium (the string) alone — only T and mu decide it. If you shake the string faster (higher frequency f), the wavelength lambda simply becomes shorter so that v = f x lambda stays the same. Amplitude (how big the shake is) does not change the speed at all.
T is the tension in the string, measured in newtons (N) — how hard the string is being pulled. mu (mu, the Greek letter) is the linear mass density: mass per unit length, mu = mass / length, in kg/m. A thick or heavy string has large mu; a thin light string has small mu. Both are properties of the string, so the speed is set before you even send the wave.
No — it increases by a factor of sqrt(2) = 1.414, not 2. Because v is proportional to sqrt(T), doubling T multiplies v by sqrt(2). To actually double the speed you must make the tension 4 times larger (since sqrt(4) = 2). NTA loves this square-root catch.
The restoring force that pulls the string back comes from tension, but the string also has inertia (its mass) resisting motion. Speed balances restoring force against inertia: v = sqrt(force property / inertia property) = sqrt(T/mu). The square root appears because it is a balance of two effects, exactly like in the pendulum and SHM formulas.
Slower. A thicker string has more mass per unit length (larger mu). Since v = sqrt(T/mu) and mu is in the denominator, larger mu means smaller v. That is why the thick low strings of a guitar vibrate slowly (low pitch) and the thin high strings vibrate fast (high pitch), for the same tension.
If the tension in a stretched string is doubled, the ratio of the initial speed to the final speed of a transverse wave along the string is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
v = sqrt(T/mu), where T is the tension in newtons and mu is the linear mass density (mass per unit length) in kg/m.
v is in m/s, T is in newtons (N), and mu is in kg/m. Check: sqrt(N / (kg/m)) = sqrt((kg m/s^2)/(kg/m)) = sqrt(m^2/s^2) = m/s. The units work out correctly.
Only through mu and T. Two strings of different material but the same tension and same linear mass density carry a transverse wave at the same speed. Material enters only by changing mass per unit length (and how much tension it can hold).
Higher wave speed on a string raises the string's frequencies (pitch). Tightening a string (more T) raises the pitch; using a thicker string (more mu) lowers it. This is exactly the sonometer law of strings used in NEET.
They describe different things. v = sqrt(T/mu) tells you the speed from the string's properties. v = f x lambda relates that same speed to frequency and wavelength. Both give the same v; the second lets you find lambda for a chosen f.
