No, the speed of sound is not the same for all inertial frames. The speed of sound is determined by the properties of the medium through which it travels, such as its density, compressibility, and temperature. In an inertial frame at rest relative to the medium, the speed of sound will have a specific value.
However, when considering different inertial frames in relative motion to each other, the speed of sound can vary. According to the principle of relativity in physics, the laws of physics should be the same in all inertial frames. But the relative motion between the source of sound and the observer can affect the perceived speed of sound due to the phenomenon known as the Doppler effect.
The Doppler effect causes a change in the perceived frequency of a wave when the source and observer are in relative motion. For sound waves, if the source is moving toward the observer, the perceived frequency increases, leading to an apparent increase in the speed of sound. Conversely, if the source is moving away from the observer, the perceived frequency decreases, resulting in an apparent decrease in the speed of sound.
In summary, the speed of sound is not the same for all inertial frames in relative motion. The actual speed of sound in a specific medium remains constant, but the perceived speed of sound can vary depending on the relative motion between the source of sound and the observer.