1. Given pressure wave

   $P = 0.01\sin(1000t-3x)\;\text{N m}^{-2}$

   Compare with the standard wave form:

   $P = P_0\sin(\omega t-kx)$

   Hence,

   $\omega = 1000\ \text{rad s}^{-1}, \qquad k=3\ \text{rad m}^{-1}$

2. Find speed of sound on the day when temperature is $0^\circ$C

   Wave speed is

   $v_0=\frac{\omega}{k}=\frac{1000}{3}\ \text{m s}^{-1} \approx 333.3\ \text{m s}^{-1}$

3. Same blade vibrating at same frequency on another day

   Since the blade is the same, the frequency remains the same. On the other day, speed of sound is given as

   $v=336\ \text{m s}^{-1}$

4. Use temperature dependence of speed of sound in air

   For air,

   $v_t \approx 332 + 0.6T$

   where $T$ is in $^\circ$C.

   At $T=0^\circ$C, speed is approximately $332\ \text{m s}^{-1}$, close to the value obtained from the wave.

   Using the change in speed form is better:

   $\Delta v = 0.6T$

   Here,

   $\Delta v = 336 - \frac{1000}{3} = 336 - 333.3 = 2.7\ \text{m s}^{-1}$

   So,

   $T = \frac{2.7}{0.6} = 4.5^\circ\text{C}$

5. Approximate value

   Closest option is

   $\boxed{4^\circ\text{C}}$

6. Check options

   • A: $12^\circ$C $\Rightarrow$ too high
   • B: $15^\circ$C $\Rightarrow$ too high
   • C: $4^\circ$C $\Rightarrow$ matches
   • D: $11^\circ$C $\Rightarrow$ too high

Therefore, the correct option is C.