Answer:

Explanation:
Given that,
Speed of transverse wave, v₁ = 20 m/s
Tension in the string, T₁ = 6 N
Let T₂ is the tension required for a wave speed of 30 m/s on the same string. The speed of a transverse wave in a string is given by :
........(1)
T is the tension in the string
is mass per unit length
It is clear from equation (1) that :





So, the tension of 13.5 N is required for a wave speed of 30 m/s. Hence, this is the required solution.
If u is about 0.2 (no unit) then the whole left side is zero.
When a problem says a rigid vessel, it means that volume is constant. At constant V, pressure and temperature are indirectly proportional. We calculate as follows:
P1/T1 = P2/T2
P1/P2 = T1/T2
P1/P2 = 273.15 / 272.15
P1/P2 = 1.00
Hope this helps. Have a nice day.