Final answer:
The resonant frequency of the spherical vase in room temperature air is 3430 Hz.
Step-by-step explanation:
To find the resonant frequency of the spherical vase, we need to consider the resonant frequency of a closed tube.
Resonant frequency of a closed tube can be calculated using the formula:
f = (v/2L)
where f is the frequency, v is the speed of sound, and L is the length of the tube.
In this case, the length of the neck is 6cm and the diameter of the neck is 4cm. So, the effective length of the tube would be 6cm + 2r (twice the radius of the neck).
Considering that the diameter is 4cm, the radius would be 2cm. Therefore, the effective length of the tube would be 6cm + (2 * 2cm) = 10cm.
Plugging in the values, we get:
f = (v/2 * 10cm)
Substituting the value of v = speed of sound in air, which is approximately 343 m/s, we can calculate the resonant frequency:
f = (343 m/s)/(2 * 10cm)
f = 3430 Hz
Therefore, the resonant frequency of this vase in room temperature air is 3430 Hz.