Date: 201910
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: VMC
Aircraft: B737 Undifferentiated or Other Model
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Takeoff / Launch
ATC / advisory: Tower ZZZ
Aircraft component: Cockpit/Cabin Communication
Component problem: Failed
Reporter organization: Air Carrier
Reporter function: Pilot Not Flying; First Officer
Reporter qualification: Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Human factors: Communication Breakdown; Situational Awareness
Second reporter function: Captain; Pilot Flying
Anomaly: Aircraft Equipment Problem Less Severe
Detector: Person Flight Attendant; Person Flight Crew
When detected: In-flight
Result: General Physical Injury / Incapacitation
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: Approximately 10 minutes after departing the Lead Flight Attendant contacted the flight crew and informed us that due to the fact that the 'flight attendants please be seated for departure' call was not made; one flight attendant who was standing in the forward galley was struck by an unsecured trash cart and had injured her back during the takeoff roll. The Lead also said that we did not make the same call while departing on our previous leg. We inquired about the injured Flight Attendant and were told that she was okay; but shaken up and sore. I; the First Officer told the Lead that both calls were made and that there must be a problem with the PA and that I would need to do a test call to determine the issue. On both calls I used the radio control panel with PA selected instead of using the center pedestal handheld microphone; and on both calls I and the Captain who was listening heard the calls made.We told the Lead that we should have been notified after departing the first time that they did not hear the call. We could have troubleshot the issue earlier and most likely prevented the second event from happening and also prevented the Flight Attendant's injury. Upon reaching cruise altitude I made a PA announcement in the same way I had previously (radio control panel); and both the Captain and I deselected our intercom to ensure we were truly hearing the call go out over the PA and not just hearing the intercom. We both heard the call go out; but when we checked with the Flight Attendant's they confirmed that they did not hear it. So I made a second call using the handheld microphone from the center pedestal; still with intercom deselected; and both the Captain and I heard the call go out again. We checked with the Flight Attendant's and the crew said they heard it but it was really faint. At this point the Captain sent a report regarding the PA system.Approximately one hour into the flight the Captain asked the injured Flight Attendant to come up to the flight deck to check up on her. Once on the flight deck the Captain had a conversation with the Flight Attendant; while I assumed control of the aircraft and ATC communications. The Flight Attendant became emotional when she started talking about being worried about having to miss work. The Captain was very supportive of her; asked her if she wanted him to coordinate medical attention for her upon our arrival into ZZZ; and advised her to seek medical attention if she needed it; but she declined. Upon our arrival into ZZZ; when the crew departed the aircraft; she seemed fine. She did not seem to be having any issues walking; pulling her bags; and was even smiling.


Second narrative: [Report narrative contained no additional information.]


Synopsis: B737 flight crew reported a problem with the intercom that resulted in a flight attendant injury during takeoff.